High-pressure structural transformations of Sn up to 138 GPa: Angle-dispersive synchrotron x-ray diffraction study

摘要

The high-pressure behavior of elemental Sn has been studied by angle-dispersive synchrotron x-ray diffraction up to 138 GPa under quasihydrostatic conditions at room temperature. The data confirm the occurrence of a first-order phase transition at 10.8 GPa between β-Sn (Sn-Ⅱ) (I4_1/amd) and a further body-centered-tetragonal polymorph (γ-Sn or Sn-Ⅲ) (I4/mmm). Above 32 GPa, this phase exhibits a distortion into a new body-centered-orthorhombic (bco) modification (Immm). Beyond 70 GPa, the structure becomes body-centered cubic (bcc) (Im-3m). There is a region of coexistence where the bcc reflections are observed to appear superimposed on the bco pattern above 40 GPa and the two diffraction signatures coexist until 70 GPa. We examined this possible existence of a kinetically hindered first-order phase transition between the two polymorphs by performing density functional theory (DFT) calculations with an emphasis on the potential energy in response to axial (c/a,b/a) distortions at constant volume. The DFT results suggest a slightly different interpretation of the structural transformations. At low pressure, the global minimum energy is always centered around b/a = 1, and there is no indication of transformation to a bco structure. However, any small strains in the c/a ratio in the system would provide an orthorhombic distortion of the observed magnitude. Such strains could be induced due to slight deviations from hydrostatic conditions in the experimental study. Concerning the possible bco-bcc phase transitions, the DFT calculations reveal an energy surface with a barrier developed between solutions with different c/a values over the pressure range of interest. Crucially, the calculated barrier heights are low, and they disappear in the region of the observed phase transformation. The DFT results indicate a mechanically softened material that may exhibit localized domain structures in response to even slightly nonhydrostatic stress conditions.